Problem 1
Themanagement of MACU Corporation istrying to determinetheamountofeachof two productsto produceoverthe comingplanningperiod. Thefollowinginformationconcernslaboravailability,laborutilization,and product profitability:
|
Department
|
Product(hours/unit)
1 2
|
Labor-Hours Available
|
|
|
A
|
1.00 0.35
|
100
|
|
B
|
0.30 0.20
|
|
36
|
|
C
|
0.20 0.50
|
|
50
|
|
Profitcontribution/unit
|
$30.00 $15.00
|
|
|
What arethe optimal (maximumprofit) productionquantities for thecompany?
a. What type/s of model/s should beused to solve theproblemand whywouldyou use that model/s?(30 points)
b. Develop a model of theMACU Corporationproblem. Solve themodel to determinethe optimal product quantities ofproducts 1 and 2.
c. Incomputingtheprofit contribution perunit, management did notdeductlaborcostsbecausetheyare considered fixed for the upcomingplanningperiod. However, supposethatovertimecan be scheduledin some ofthe departments.Which department would yourecommend schedulingforovertime? Howmuch wouldyou bewillingtopayper hourof overtimein each department?
d. Supposethat 10, 6,and 8 hours of overtime maybescheduled in departments A,
B, and C respectively. The cost perhour ofovertime is $18in departmentA,
$22.50 in departmentB,and $12 in departmentC. Formulate amodelthat can be used to determine the optimal production quantities if overtime ismade available.What arethe optimal product quantities, and whatistherevised total contribution to profit? Howmuch overtime doyourecommend usingin each department? What is the increasein thetotal contribution to profit if overtime is used?